Chapter 7 - Applications of Trigonometry and Vectors - Section 7.2 The Ambiguous Case of the Law of Sines - 7.2 Exercises - Page 304: 12

$B = 30^{\circ}$

We can use the law of sines to find the angle $B$: $\frac{a}{sin~A} = \frac{b}{sin~B}$ $sin~B = \frac{b~sin~A}{a}$ $sin~B = \frac{(3)~sin~(45^{\circ})}{3\sqrt{2}}$ $sin~B = \frac{(3)~(\frac{\sqrt{2}}{2})}{3\sqrt{2}}$ $sin~B = \frac{1}{2}$ $B = arcsin(\frac{1}{2})$ $B = 30^{\circ}$